Maybe i'm beating a dead horse here, but i think the variety() command
has another bug in it (different from
http://trac.sagemath.org/sage_trac/ticket/4622
). It crashes when working over number fields with the optional
command 'ring=QQbar', possibly because it doesn't first embed the
number field into QQbar. Here are two examples.
Alex
sage: var('t')
t
sage: K= NumberField(t^2+2,'a')
sage: R.<x,y>= PolynomialRing(K)
sage: I= R.ideal([ x*y - 1, (x-2)^2 + (y-1)^2 - 1])
sage: I= R.ideal(I.groebner_basis())
sage: I.dimension()
0
sage: I.variety(ring=QQbar)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
/Users/arai021/<ipython console> in <module>()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/multi_polynomial_ideal.pyc in variety(self, ring)
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/multi_polynomial_ideal.pyc in _variety(T, V, v)
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.roots (sage/rings/
polynomial/polynomial_element.c:25078)()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial.change_ring (sage/
rings/polynomial/polynomial_element.c:13768)()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/
structure/parent.so in sage.structure.parent.Parent.__call__ (sage/
structure/parent.c:3653)()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/
structure/coerce_maps.so in
sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (sage/
structure/coerce_maps.c:2793)()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/
structure/coerce_maps.so in sage.structure.coerce_maps._call_ (sage/
structure/coerce_maps.c:2700)()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_ring.pyc in _element_constructor_(self, x,
check, is_gen, construct, **kwds)
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_element_generic.pyc in __init__(self, parent, x,
check, is_gen, construct)
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
polynomial/polynomial_element.so in
sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.__init__
(sage/rings/polynomial/polynomial_element.c:29264)()
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
qqbar.pyc in __call__(self, x)
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
qqbar.pyc in __init__(self, x)
/Applications/sage-3.3/local/lib/python2.5/site-packages/sage/rings/
qqbar.pyc in __init__(self, parent, x)
TypeError: Illegal initializer for algebraic number
----------------------------------------------------------------------------------------------------------
sage: K= NumberField(t^2+2,'a')
sage: R.<x,y>= PolynomialRing(K)
sage: I= R.ideal([ x*y - 1, (x-2)^2 + (y-1)^2 - 1])
sage: I= R.ideal(I.groebner_basis())
sage: I.dimension()
0
sage: I.variety()
[{y: 1, x: 1}]
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